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Properties

Label 7.12-4.0.2-2-2-2-2-2.1
Genus \(7\)
Quotient genus \(0\)
Group \(D_6\)
Signature \([ 0; 2, 2, 2, 2, 2, 2 ]\)
Generating Vectors \(4\)

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Family Information

Genus: $7$
Quotient genus: $0$
Group name: $D_6$
Group identifier: $[12,4]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2 ]$
Conjugacy classes for this refined passport: $2, 2, 3, 3, 3, 3$

Jacobian variety group algebra decomposition:$E\times A_{2}\times A_{2}^{2}$
Corresponding character(s): $2, 3, 6$

Other Data

Hyperelliptic curve(s):no
Cyclic trigonal curve(s):no

Generating vector(s)

Displaying 4 of 4 generating vectors for this refined passport.

7.12-4.0.2-2-2-2-2-2.1.1

  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)

7.12-4.0.2-2-2-2-2-2.1.2
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,8) (2,7) (3,9) (4,11) (5,10) (6,12)

7.12-4.0.2-2-2-2-2-2.1.3
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)

7.12-4.0.2-2-2-2-2-2.1.4
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
  (1,8) (2,7) (3,9) (4,11) (5,10) (6,12)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)

Display number of generating vectors:

Displaying the unique representative of this refined passport up to braid equivalence.

  7.12-4.0.2-2-2-2-2-2.1.1

  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
  (1,9) (2,8) (3,7) (4,12) (5,11) (6,10)